A1 for 25 2 B2 for all 4 correct

Transcription

1 1 2x + 2(x + 9) < 200 2x + 2x + 18 < 200 4x + 18 < 200 4x < 182 x < B1 for x + 9 oe seen (it could just be on a diagram) or any rectangle with length 9 cm greater than width M1 for 2x + 2(x + 9) oe A1 for 45.5 B1 for answer of = = = = = 45.5 M1 for (=50) M1 for (9 + 9) 4 (=4.5) A1 for 45.5 B1 for answer of = A and 25 2 M1 for (= 87) or 7 16 (=112) or (= 9) or (= 10.5) B and 2 C and 4 D and 1 A1 for 25 2 B2 for all 4 correct (B1 for 2 correct) 1MA1 practice paper 2H (Set 6) mark scheme: Version 1.0 1

2 4 (a) 7.5 M1 for 4.5² + 6² (=5 6.25) (b) M1 for or (4.5² + 6²) A1 for 7.5 M1 for use of appropriate trig ratio eg tan CAB = sin CAB = "7.5" ( = 0.6), cos CAB = 6 "7.5" ( = 0.8) M1 for inverse trig shown correctly e.g. CAB = tan ( = 0.75), CAB = sin "7.5" ( = 0.6), CAB = cos 1 6 "7.5" ( = 0.8) A1 for 6.8 to 7 (or 5 to 5.2 if identified as ACB) B1ft for bearing if 6.8 is not x 2 + 7x 2 4 M1 for finding an expression for a missing length eg 4x 1 x x (=2x 1) or x+ 2 2x (= 2 x) ( = 0.75), M1 for a correct expression for one area from the cross-section, eg. x 2x or (4x 1)( x + 2 2x) or for one volume of cuboid(s), eg. x 2x (x + 1) M1 for a complete method to find the volume A1 for 9x 2 + 7x 2 or (9x 2)(x + 1) oe 1MA1 practice paper 2H (Set 6) mark scheme: Version 1.0 2

3 6 8 4 M1 for (2 10 ) (= 6) A1 for (CD =) 6 M1 (dep on M1) for ( 6 2) 4 C1 for area of 8 from fully correct working (014 ) B1 for 7.75 or7.85 or 5.15 or 5.25 or 62.5 or 6.5 M1 for sin 62.5 A1 for 17.7( ) 8 (a) Negative 1 B1 cao (b) M1 for a line of best fit drawn between (9, 10) & (9, 140) and between (1, 100) & (1,110) inc.. A1 for inclusive 1MA1 practice paper 2H (Set 6) mark scheme: Version 1.0

4 9 4x + y = 695 5x + 2y = 720 Coffee 1.1(0) Tea 85p 5 M1 for attempt to use variables for cost of cup of tea and cost of a cup of coffee. A1 for correct equations : 4x + y = 695 and 5x + 2y = 720 oe 8x + 6y = x + 6y = x = 770 x = 110 y = 85 M1 for correct process to eliminate either x or y (condone one arithmetic error) could be by multiplication of both equations and then addition/subtraction or by manipulation of one equation and then substitution into second equation M1 (dep) for substituting found value into either equation A1 for correct answers with units 10 2 = k 1 ½ 2 M1 for reading off and substituting a pair of values from the graph (excluding 0, 1) into the equation, eg x = 1, y = 2 A1 for ½ oe 1MA1 practice paper 2H (Set 6) mark scheme: Version 1.0 4

5 11 US Correct conclusion 5 M1 for a conversion, gallons to litres or litres to gallons 1 gal costs =$.48 based on correct calculations 1 litre costs $ = $ I litre costs Euros = Euros Russia 1 litre costs = Roubles 1 litre costs Euros = Euros Or litres = = US gallons 800 roubles = ( ) 0.77 = $ Cost in $ of 1 US gallon in Russia is = $ Cost in $ of 1 US gallon in US = = $.48 M1 for a conversion, roubles to US Dollars or US Dollars to roubles or convert both to Euros M1 for a conversion to common units and common currency A1 for two correct answers in the same currency and for the same unit C1 (dep on at least M1) for correct conclusion ft candidate's figures. eg M1 1 US gal costs (=.48) M1 1 litre costs (= ) M1 1 litre in Russia costs (=0.769) A1 for and C1 (dep on at least M1) for correct conclusion ft candidate's figures. 1MA1 practice paper 2H (Set 6) mark scheme: Version 1.0 5

6 Cost per litre for US petrol $0.918 or or 28.7 rub Cost per gallon for US petrol $.48 or 2.68 or 109 rub Cost per litre for Russian petrol 1.27 rub or or $1 Cost per gallon for Russian petrol 118 rub or 2.92 or $ (a) 0. 0., 0.7, 0. 2 B1 for 0. as first spin oe B1 for 0., 0.7, 0. in correct positions for second spin oe (b) 0.42 M1 for or (=0.21) M1 for ( M2 for ) A1 for 0.42 oe 1MA1 practice paper 2H (Set 6) mark scheme: Version 1.0 6

7 1 (A =) 0.5 (4 + k) (k =) M (k 4) oe (= 5 6) oe k + 4 = (10 6)/ (k =) 2 (5 6)/ 4 or (k =) (5 6 )/(0.5 ) oe M1 correctly isolating k A1 Accept 2(5 2 2) but don't accept followed by M1 for π (= ) ' ' M1 (dep) for 2 π 5.8 A1 for M1 for or or 0.89(2 ) or 1.12(06896 ) 5.8 M1 for A1 for or MA1 practice paper 2H (Set 6) mark scheme: Version 1.0 7

8 15 (n 2 + 4n + 4) (n 2 +2n +1) Proof 4 M1 for correct method to expand (n + 2)² or (n + 1)² 2n + 2n 2 + n 2n + n(2n + ) M1 for correct simplification of numerator M1 for factorisation of 2n² + n or for clearing the fractions on both sides correctly C1 for complete and correct proof M1 for { ( n + 2) ( n +1) }{ ( n + 2) + ( n +1) } M1 for 1 ( 2n + ) M1 for factorisation of 2n² + n or for clearing the fractions on both sides correctly C1 for complete and correct proof M1 for n{ ( n + 2) M1 for n ( n + 2) ( n + 2) 2 ( n +1 ) 2 M1 for correct expansion of n{ ( n + 2) 2 ( n +1 ) 2 } 2 ( n +1 ) 2 } = (2n² + n) 1 2 n ( n +1 ) 2 or for correct expansion of C1 for complete and correct proof (must include statement recognising the equality of LHS and RHS) 1MA1 practice paper 2H (Set 6) mark scheme: Version 1.0 8

9 16 p( r ) = 2r + 5 p M1 for multiplying both sides by r pr p = 2r + 5 p 2 eg p( r ) or pr p or pr or p r pr 2r = p + 5 r(p 2) = p + 5 M1 for isolating their two terms in r on one side of an equation to get pr 2r or 2r pr M1 (dep on M1) for correctly factorising r from pr 2r A1 for 17 (a) y f(x 5) 1 B1 cao (b) (4, ) 2 B2 cao p + 5 p 2 or p 5 oe 2 p (B1 for one coord. correct (in correct position) or (,4).) 18 (a) 1.5 B1 for tangent drawn at t = 8 M1 for height base for a triangle with the tangent as hypotenuse A1 for 1.25 to 1.75 (b) 156 M1 for attempting to find area under curve M1 for correct method to find the area under the curve between t = 0 and t = 6 (at least areas) A1 for MA1 practice paper 2H (Set 6) mark scheme: Version 1.0 9

10 k M1 for S α or S = 16 t t 20 Gradient of N = Gradient of perpendicular to line N = 1 M1 for 1 2 = k 2 oe or S = 4 t 2 M1 S = 8 oe A1 for 1 16 oe 1 M1 for complete method to find gradient of line N or for y = x + 1 drawing a perpendicular line M1 for method to find the gradient of a perpendicular line 1 A1 y = x + 1 oe 21 p = 8, q = 10 M1 for finding the difference between the x or y coordinates eg 4 2 (= 2) or 17 5 (= 12) M1 for a complete method to find the values of p or q A1 cao 1MA1 practice paper 2H (Set 6) mark scheme: Version

11 National performance data from Results Plus Original source of questions Mean score of students achieving grade: Qn Spec Paper Session YYMM Qn Topic Max score ALL A* A B C D E 1 5MM2 2F 1106 Q2 Bounds H 120 Q02 Mean, median, mode H 1011 Q11 Distance-time / travel graphs MA0 2H 1406 Q15 Pythagoras in 2D MA0 1H 1611 Q22 Volume 4 Data to be added in January MA0 1H 1611 Q26 Area 5 Data to be added in January MA0 2H 1611 Q20 Bounds Data to be added in January H 911 Q11 Scatter diagrams AM1 1H 106 Q21 Simultaneous equations MA0 2H 1611 Q22a Exponential graphs 2 Data to be added in January AM1 1H 1406 Q21 Conversions MA0 2H 1411 Q19 Probability tree diagrams MA0 1H 1405 Q18 Surds MA0 2H 111 Q24 Volume MA0 2H 1611 Q24 4 Data to be added in January MM2 2H 1211 Q26 Rearranging equations H 1006 Q27 Transformation of functions AM2 2H 106 Q18 Area under a curve MM2 2H 1411 Q19 Direct and indirect proportion MA0 2H 1506 Q17 Gradients MA0 2H 1506 Q12 Coordinates in 2D MA1 practice paper 2H (Set 6) mark scheme: Version